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New Music Concepts 2020

3-Dimensional Motif Modeling for Music Composition

Part of the New Music Concepts book series (NMC volume 7)
ISBN: 978-88-944350-3-0

Author(s): Shigeki Sagayama, Hitomi Kaneko

Abstract: This paper discusses a principle of handling notes and motifs in 3-dimensional (3D) space as a technique towards a new method of music composition. In European classical music, a relatively small number of motifs are repeatedly used to form entire music pieces or movements by repeating, imitating and transposing the primary motifs. Moreover, these motifs are sometimes inverted, reversed, lengthened or shortened. To generalize this principle of motif manipulation operations, we begin with a short discussion of a 2-dimensional affine transformation representation, and develop this idea into a formalization of notes in a music score as triplets of the onset time, pitch and note duration, equivalent to vectors (x, y, z) in 3-dimensional space. Thus, a set of notes, often referred to as a motif, subject, object, fragment, chord, figure, etc. depending on the context, can be represented by a set of points forming an object in 3-dimensional space. Rotation of such an object yields countless variants of note sequences from various rotation angles. This new approach was applied to music composition of several pieces for performance in commercial concerts, some being scheduled for publication.

Keywords: 3-dimensional note space, melodic motifs, rotation, affine transformation, music composition